Consistent Initialization of Sensitivity Matrices for a Class of Parametric DAE Systems

Abstract

A class of parametric semi-explicit differential algebraic equation (DAE) systems up to index 2 is considered. It is well known that initial value problems with DAE systems do not have a solution for every initial value. The initial value has to be consistent. Therefore, a method for the calculation of consistent initial values for this class of systems is introduced. In addition, various applications need information about the dependency of the solution of an initial value problem with respect to given parameters. This question leads to a linear matrix DAE system, the sensitivity DAE system, for which consistent initial values have to be provided as well. An appropriate consistent initialization method based on the solution differentiability of parametric nonlinear optimization problems in combination with Newton's method is developed. An illustrative example shows the capability of the method.